From e23c1ffb41979feed815dc18a7b7d7f94bcefe2a Mon Sep 17 00:00:00 2001 From: Fabrice Mouhartem Date: Tue, 20 Mar 2018 11:09:07 +0100 Subject: [PATCH] Uniformize notation --- sec-pairings.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/sec-pairings.tex b/sec-pairings.tex index 179416b..b9eb309 100644 --- a/sec-pairings.tex +++ b/sec-pairings.tex @@ -33,7 +33,7 @@ This hypothesis, from which the Diffie-Hellman key exchange relies its security The \emph{Symmetric eXternal Diffie-Hellman} ($\SXDH$) assumption holds if the $\DDH$ assumption holds both in $\GG$ and $\Gh$. \end{definition} -In Chapter~\ref{ch:sigmasig}, the security of the group signature scheme relies on the $\SXDH$ assumption, which is a well-studied assumption. +In \cref{ch:sigmasig}, the security of the group signature scheme relies on the $\SXDH$ assumption, which is a well-studied assumption. Moreover, this assumption is static, meaning that the size of the assumption is independent of any parameters, and is non-interactive, in the sense that it does not involve any oracle. This gives a stronger security guarantee for the security of schemes proven under this kind of assumptions. @@ -43,8 +43,8 @@ In the aforementioned chapter, we also rely on the following assumption, which g \begin{definition}[$\SDL$] \label{de:SDL} \index{Pairings!SDL} - In bilinear groups $(\GG,\hat{\GG},\GT^{})$ of prime order $p$, the \emph {Symmetric Discrete Logarithm} ($\SDL$) problem consists in, given - $(g,\hat{g},g^a,\hat{g}^a) \in \GG \times \hat{\GG}$ + In bilinear groups $(\GG,\Gh,\GT^{})$ of prime order $p$, the \emph {Symmetric Discrete Logarithm} ($\SDL$) problem consists in, given + $(g,\hat{g},g^a,\hat{g}^a) \in \GG \times \Gh$ where $a \sample \ZZ_p^{}$, computing $a \in \ZZ_p^{}$. \end{definition}